Question

The expected number of tosses until the first head appears, given that head occurs with probability $p$, is \(\underline{\hspace{1cm}}\).

• A. $p/(1-p)$
• B. $(1-p)/p$
• C. $1/p$
• D. $1/p^2$

Hint:

The geometric distribution models repeated trials until first success; its expectation is always $1/p$.

Answer 1

The Correct Option is C

The experiment follows a geometric distribution where the probability of success (head) is $p$.
For a geometric random variable $X$ counting the number of trials until the first success:
$\mathbb{E}[X] = 1/p$.
Thus the expected number of tosses required to get the first head is $1/p$.
Final Answer: $1/p$